A Maker-Breaker game is a kind of positional game. Like most positional games, it is described by its set of positions/points/elements () and its family of winning-sets (- a family of subsets of ). It is played by two players, called Maker and Breaker, who alternately take previously-untaken elements. In a Maker-Breaker game, Maker wins if he manages to hold all the elements of a winning-set, while Breaker wins if he manages to prevent this, i.e. to hold at least one element in each winning-set. Draws are not possible. In each Maker-Breaker game, either Maker or Breaker has a winning strategy. The main research question about these games is which of these two options holds. Examples A classic Maker-Breaker game is Hex. There, the winning-sets are all paths from the left side of the board to the right side. Maker wins by owning a connected path; Breaker wins by owning a connected path from top to bottom, since it blocks all connected paths from left to right. Tic-tac-toe can be played as a Maker-Breaker game: in that variant, the goal of Maker is to pick 3 squares in a row, and the goal of Breaker is just to prevent Maker from doing so. In that variant, Maker has a winning strategy. This is in contrast to the classic variant (which is a Strong positional game) where the second player has a drawing strategy (see Strong positional game#Comparison to Maker-Breaker game). Unordered CNF Game on a positive CNF (all positive literals) can be considered as a Maker-Breaker game where Maker wants to falsify the CNF, and Breaker wants to satisfy it. Some research has been done on playing Maker-Breaker games when the board of the game is the edge set of some graph (usually taken as a complete graph), and the family of winning-sets is , where is some graph property (usually taken to be monotone increasing [clarify?]) such as connectivity. For instance, the Shannon switching game is a Maker-Breaker game in which the winning sets are the paths between two distinguished vertices. Breaker-Maker duality In a Maker-Breaker game, usually Maker plays first. But it is also possible to let Breaker play first. Playing first is always advantageous: any winning strategy for Maker playing second on yields a winning strategy for Maker playing first on The same is true for Breaker. Moreover, for every game we can define its transversal game